It seems to be a bit of hit and miss with various FLD's around the country when it comes to using big bores in the UK. I know there's people around who have the .375 for UK use, I actually know someone with a .416 for use on UK boar, however, there's some regions that won't even consider the .375 or upwards for anything other than 'sport abroad'. It seems rather pointless as bigger doesn't always mean more "dangerous", in fact, many 'big bores' actually a have limited trajectory and are really intended for close range work.
I found a very nice 450 Marlin in bolt action form by Mannlicher, and I think it'd be perfect for boar and Sika/Fallow. It does fire a large heavy bullet, but the velocity of this round is fairly low and can cause little meat damage if loaded correctly.